{"id":333,"date":"2018-06-30T11:56:33","date_gmt":"2018-06-30T02:56:33","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-calculate-vif-by-r\/"},"modified":"2024-10-14T11:44:48","modified_gmt":"2024-10-14T02:44:48","slug":"how-to-calculate-vif-by-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-calculate-vif-by-r\/","title":{"rendered":"R \u3067\u591a\u91cd\u5171\u7dda\u6027\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b\u305f\u3081\u306b VIF \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u91cd\u56de\u5e30\u5206\u6790\u3067\u3001\u5909\u6570\u9078\u629e\u306b\u304a\u3044\u3066\u3001\u8003\u616e\u3057\u306a\u3044\u3068\u3044\u3051\u306a\u3044\u306e\u304c\u3001\u591a\u91cd\u5171\u7dda\u6027\u3002<\/p>\n\n\n\n

\u591a\u91cd\u5171\u7dda\u6027\u306e\u30c1\u30a7\u30c3\u30af\u306f\u7d71\u8a08\u30bd\u30d5\u30c8R\u3067\u3069\u3046\u3084\u308b\u306e\u304b\uff1f<\/p>\n\n\n\n\n\n\n\n

\u591a\u91cd\u5171\u7dda\u6027\u3068\u306f\u4f55\u304b\uff1f<\/h2>\n\n\n\n

\u751f\u307e\u308c\u305f\u897f\u66a6\u5e74\u3068\u5e74\u9f62\u306f\u3001\u3069\u306e\u304f\u3089\u3044\u76f8\u95a2\u3059\u308b\u3060\u308d\u3046\u304b\uff1f<\/p>\n\n\n\n

\u5168\u304f\u4e00\u81f4\u3059\u308b\u3068\u3044\u3063\u3066\u3082\u8a00\u3044\u3002<\/p>\n\n\n\n

\u751f\u307e\u308c\u305f\u6708\u306b\u3088\u3063\u3066\u540c\u3058\u5e74\u306b\u751f\u307e\u308c\u305f\u4eba\u3067\u3082\u3001\u5c0b\u306d\u305f\u65e5\u306b\u3088\u3063\u3066\u5e74\u9f62\u304c1\u6b73\u9055\u3046\u3060\u3051\u3060\u3002<\/p>\n\n\n\n

\u751f\u307e\u308c\u305f\u897f\u66a6\u5e74\u3068\u5e74\u9f62\u3068\u75c5\u6c17\u3068\u306e\u95a2\u4fc2\u3092\u540c\u6642\u306b\u898b\u3088\u3046\u3068\u3059\u308b\u3068\u898b\u3089\u308c\u308b\u3060\u308d\u3046\u304b\uff1f<\/p>\n\n\n\n

\u7b54\u3048\u306f\u3001\u898b\u3089\u308c\u306a\u3044\u3002<\/p>\n\n\n\n

\u5168\u304f\u540c\u3058\u304b\u3082\u306e\u3059\u3054\u304f\u76f8\u95a2\u304c\u5f37\u3044\u5909\u6570\u540c\u58eb\u3067\u306f\u3001\u540c\u6642\u306b\u95a2\u4fc2\u6027\u3092\u898b\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n

\u306a\u305c\u306a\u3089\u3001\u3069\u3061\u3089\u304b\u4e00\u65b9\u3067\u4e8b\u8db3\u308a\u308b\u304b\u3089\u3060\u3002<\/p>\n\n\n\n

\u540c\u6642\u306b\u898b\u3088\u3046\u3068\u3059\u308b\u3068\u3001\u540c\u3058\u95a2\u4fc2\u3092\u6301\u3063\u3066\u3044\u308b\u306e\u306b\u3001\u771f\u9006\u306e\u7d50\u679c\u304c\u51fa\u305f\u308a\u3059\u308b\u3002<\/p>\n\n\n\n

\u591a\u5909\u91cf\u30e2\u30c7\u30eb\u5185\u3067\u3001\u30d0\u30e9\u30f3\u30b9\u3092\u3068\u308b\u305f\u3081\u3060\u3002<\/p>\n\n\n\n

\u3053\u306e\u3088\u3046\u306b\u975e\u5e38\u306b\u9ad8\u3044\u76f8\u95a2\u304c\u3042\u3063\u3066\u3001\u540c\u6642\u306b\u540c\u3058\u591a\u5909\u91cf\u30e2\u30c7\u30eb\u3067\u306f\u3076\u3064\u304b\u308a\u3042\u3063\u3066\u3001\u9593\u9055\u3063\u305f\u7b54\u3048\u3092\u5c0e\u304d\u51fa\u3057\u3066\u3057\u307e\u3046\u306e\u304c\u3001\u591a\u91cd\u5171\u7dda\u6027\u3060\u3002<\/p>\n\n\n\n

\u591a\u91cd\u5171\u7dda\u6027\u306e\u30c1\u30a7\u30c3\u30af\u306fR\u3067\u3069\u3046\u3084\u308b\u304b\uff1f<\/h2>\n\n\n\n

\u5206\u6563\u62e1\u5927\u4fc2\u6570 Variance Inflation Factor (VIF)\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

$$ VIF = \\frac{1}{1 – R_j^2} $$<\/p>\n\n\n\n

$ R_j^2 $ \u306f\u3001\u8aac\u660e\u5909\u6570 j \u3092\u76ee\u7684\u5909\u6570\u3068\u307f\u306a\u3057\u3001\u4ed6\u306e\u3059\u3079\u3066\u306e\u8aac\u660e\u5909\u6570\u3067\u4e88\u6e2c\u3057\u305f\u3068\u304d\u306e\u6c7a\u5b9a\u4fc2\u6570\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u3053\u308c\u304c5\u3088\u308a\u5927\u304d\u3044\u3068\u591a\u91cd\u5171\u7dda\u6027\u304c\u7591\u308f\u308c\u308b\u3002<\/p>\n\n\n\n

10\u3088\u308a\u5927\u304d\u3044\u3068\u591a\u91cd\u5171\u7dda\u6027\u304c\u78ba\u5b9a\u7684\u3060\u3002<\/p>\n\n\n\n

\u5bfe\u51e6\u306f\u3001VIF\u304c\u5927\u304d\u3044\u5909\u6570\u3092\u591a\u5909\u91cf\u30e2\u30c7\u30eb\u304b\u3089\u306f\u305a\u3059\u3053\u3068\u3002<\/p>\n\n\n\n

\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n\"\"<\/a>\r\n

\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>

R\u306bVIF\u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570<\/h2>\n\n\n\n

car\u30d1\u30c3\u30b1\u30fc\u30b8\u306bvif()\u3068\u3044\u3046\u95a2\u6570\u304c\u3042\u308b\u3002<\/p>\n\n\n\n

\u91cd\u56de\u5e30\u5206\u6790 lm() \u3084\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790 glm() \u306e\u7d50\u679c\u3092\u6295\u5165\u3059\u308b\u3060\u3051\u3067\u3001\u591a\u91cd\u5171\u7dda\u6027\u306e\u30c1\u30a7\u30c3\u30af\u7d50\u679c\u3092\u8fd4\u3057\u3066\u304f\u308c\u308b\u3002<\/p>\n\n\n\n

vif()\u306e\u3059\u3054\u3044\u3068\u3053\u308d\u306f\u3001\u9023\u7d9a\u91cf\u3060\u3051\u3067\u306a\u304f\u3001\u30ab\u30c6\u30b4\u30ea\u3082\u540c\u6642\u306b\u6271\u3048\u308b\u3053\u3068\u3002<\/p>\n\n\n\n

Duncan\u3068\u3044\u3046\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u3001income\u3068education\u306eVIF\u306f2\u8d85\u3067\u3001\u591a\u91cd\u5171\u7dda\u6027\u306e\u6050\u308c\u306f\u306a\u3044\u3002<\/p>\n\n\n\n

library<\/span>(<\/span>car)<\/span> #\u4f7f\u3046\u3068\u304d\u306b\u6bce\u56de<\/span>\nlm.res1 <-<\/span> lm<\/span>(<\/span>prestige ~<\/span> income +<\/span> education,<\/span> data=<\/span>Duncan)<\/span>\nvif<\/span>(<\/span>lm.res1)<\/span>\n1<\/span>\/<\/span>(<\/span>1<\/span>-<\/span>cor<\/span>(<\/span>Duncan[,<\/span>2<\/span>:<\/span>3<\/span>])<\/span>^<\/span>2<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u9023\u7d9a\u5909\u6570\uff12\u3064\u3060\u3051\u306e\u5834\u5408\u3001\u6c7a\u5b9a\u4fc2\u6570\u306f\u3001\u76f8\u95a2\u4fc2\u6570\u306e2\u4e57\u3068\u4e00\u81f4\u3059\u308b\u306e\u3067\u30011\/(1-cor()2<\/sup>) \u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
><\/span> vif<\/span>(<\/span>lm.res1)<\/span>\nincome education\n2.1049<\/span>    2.1049<\/span>\n><\/span> 1<\/span>\/<\/span>(<\/span>1<\/span>-<\/span>cor<\/span>(<\/span>Duncan[,<\/span>2<\/span>:<\/span>3<\/span>])<\/span>^<\/span>2<\/span>)<\/span>\nincome education\nincome       Inf<\/span>    2.1049<\/span>\neducation 2.1049<\/span>       Inf<\/span>\n<\/code><\/pre>\n\n\n\n
type\u3068\u3044\u3046\u30ab\u30c6\u30b4\u30ea\u5909\u6570\u3092\u5165\u308c\u308b\u3068\u3069\u3046\u306a\u308b\u304b\uff1f<\/p>\n\n\n\n
><\/span> summary<\/span>(<\/span>Duncan)<\/span>\ntype        income        education         prestige\nbc  :<\/span>21<\/span>   Min.   :<\/span> 7.00<\/span>   Min.   :<\/span>  7.00<\/span>   Min.   :<\/span> 3.00<\/span>\nprof:<\/span>18<\/span>   1st Qu.:<\/span>21.00<\/span>   1st Qu.:<\/span> 26.00<\/span>   1st Qu.:<\/span>16.00<\/span>\nwc  :<\/span> 6<\/span>   Median :<\/span>42.00<\/span>   Median :<\/span> 45.00<\/span>   Median :<\/span>41.00<\/span>\nMean   :<\/span>41.87<\/span>   Mean   :<\/span> 52.56<\/span>   Mean   :<\/span>47.69<\/span>\n3rd Qu.:<\/span>64.00<\/span>   3rd Qu.:<\/span> 84.00<\/span>   3rd Qu.:<\/span>81.00<\/span>\nMax.   :<\/span>81.00<\/span>   Max.   :<\/span>100.00<\/span>   Max.   :<\/span>97.00<\/span>\n<\/code><\/pre>\n\n\n\n
Generalized VIF (GVIF)\u304c\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
lm.res2 <-<\/span> lm<\/span>(<\/span>prestige ~<\/span> income +<\/span> education +<\/span> type,<\/span> data=<\/span>Duncan)<\/span>\nvif<\/span>(<\/span>lm.res2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u9023\u7d9a\u91cf\u306f\u81ea\u7531\u5ea61\u3002<\/p>\n\n\n\n
\u30ab\u30c6\u30b4\u30ea\u306f\u30ab\u30c6\u30b4\u30ea\u6570\u306b\u5fdc\u3058\u3066\u81ea\u7531\u5ea6\u304c\u6c7a\u307e\u308b\u3002type\u306f3\u30ab\u30c6\u30b4\u30ea\u3067\u3001\u81ea\u7531\u5ea62\u3002<\/p>\n\n\n\n
\u81ea\u7531\u5ea6\u3067\u8abf\u6574\u3057\u305f GVIF^(1\/(2*Df))<\/code> \u3092\u898b\u308b\u3079\u304d\u3002<\/p>\n\n\n\n
><\/span> vif<\/span>(<\/span>lm.res2)<\/span>\nGVIF Df GVIF^<\/span>(<\/span>1<\/span>\/<\/span>(<\/span>2<\/span>*<\/span>Df))<\/span>\nincome    2.209178<\/span>  1<\/span>        1.486330<\/span>\neducation 5.297584<\/span>  1<\/span>        2.301648<\/span>\ntype      5.098592<\/span>  2<\/span>        1.502666<\/span>\n<\/code><\/pre>\n\n\n\n
VIF\u306e\u57fa\u6e96\u306e10\u306f\u3069\u306e\u304f\u3089\u3044\u306e\u76f8\u95a2\u30ec\u30d9\u30eb\u304b\uff1f<\/h2>\n\n\n\n
\u305d\u3082\u305d\u3082VIF\u304c10\u306e\u5834\u5408\u3001\u76f8\u95a2\u4fc2\u6570\u3060\u3068\u3001\u3044\u304f\u3064\u306b\u306a\u308b\u304b\uff1f<\/p>\n\n\n\n
\u3053\u308c\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u3067\u3001VIF\u306e\u57fa\u6e96\u304c\u30a4\u30e1\u30fc\u30b8\u3057\u3084\u3059\u304f\u306a\u308b\u306f\u305a\u3060\u3002<\/p>\n\n\n\n
10 = 1\/(1-r2<\/sup>)<\/p>\n\n\n\n
1\/10 = 1-r2<\/sup><\/p>\n\n\n\n
r2<\/sup> = 0.9<\/p>\n\n\n\n
r \u2252 \u00b10.95<\/p>\n\n\n\n
0.95\u3068\u3044\u3046\u3053\u3068\u306f\u307b\u3068\u3093\u3069\u3074\u3063\u305f\u308a\u4e00\u81f4\u3057\u3066\u3044\u308b\u72b6\u614b\u3002<\/p>\n\n\n\n
\u30ab\u30c6\u30b4\u30ea\u3068\u306e\u76f8\u95a2\u306e\u5834\u5408\u306f\u3001\u30ab\u30c6\u30b4\u30ea\u3054\u3068\u306b\u542b\u307e\u308c\u308b\u6570\u5b57\u304c\u5168\u7136\u9055\u3046\u3088\u3046\u306a\u5834\u5408\u304b\u3002<\/p>\n\n\n\n
\u4f8b\u3048\u3070\u3001\u30ab\u30c6\u30b4\u30ea<\/p>\n\n\n\n
\uff11\uff0c\uff12\uff0c\uff13\uff0c\uff14\uff0c\uff15\u304c\u3001
10\u4ee3\u300120\u4ee3\u300130\u4ee3\u300140\u4ee3\u300150\u4ee3\u3068\u3001<\/p>\n\n\n\n
\u307b\u307c\u5404\u5e74\u4ee3\u306b\u5206\u304b\u308c\u3066\u3057\u307e\u3046\u3088\u3046\u306a\u5834\u5408\u3001\u4e0d\u9069\u5207\u3068\u3044\u3046\u3053\u3068\u3060\u308d\u3046\u3002<\/p>\n\n\n\n
\u305d\u308c\u4ee5\u5916\u306a\u3089\u3001\u307e\u305a\u554f\u984c\u306b\u306a\u3089\u306a\u3044\u3068\u8003\u3048\u308c\u3070\u3044\u3044\u3068\u601d\u3046\u3002<\/p>\n\n\n\n
\u3061\u306a\u307f\u306bVIF\uff1d5\u306e\u5834\u5408\u306f\u3001r2<\/sup> = 0.8 \u3064\u307e\u308a r \u2252 \u00b10.89 \u3067\u3001\u76f8\u95a2\u4fc2\u6570\u306f\u3060\u3044\u305f\u30440.9\u304f\u3089\u3044\u3002<\/p>\n\n\n\n
VIF = 3\u306e\u5834\u5408\u306f\u3001r2<\/sup> = 0.67 \u3064\u307e\u308a r \u2252 \u00b10.82 \u3067\u3001\u76f8\u95a2\u4fc2\u6570\u306f\u3060\u3044\u305f\u30440.8\u304f\u3089\u3044\u3002<\/p>\n\n\n\n
\u95be\u5024\uff08\u3057\u304d\u3044\u3061\uff09\u5019\u88dc\u3068\u3057\u3066\u30013, 5, 10\u306e\u76f8\u95a2\u4fc2\u6570\u306e\u30a4\u30e1\u30fc\u30b8\u3092\u3082\u3063\u3066\u304a\u3051\u3070\u3044\u3044\u306e\u3067\u306f\u306a\u3044\u304b\u3002<\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u91cd\u56de\u5e30\u5206\u6790\u3084\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790\u3067\u3001\u591a\u5909\u91cf\u30e2\u30c7\u30eb\u3092\u89e3\u6790\u3059\u308b\u5834\u5408\u3001\u72ec\u7acb\u5909\u6570\u540c\u58eb\u306e\u76f8\u95a2\u304c\u5f37\u3059\u304e\u308b\u3068\u3001\u9069\u5207\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u306a\u3044\u3002<\/p>\n\n\n\n
\u72ec\u7acb\u5909\u6570\u540c\u58eb\u306e\u76f8\u95a2\u304c\u5f37\u3059\u304e\u308b\u72b6\u614b\u3092\u591a\u91cd\u5171\u7dda\u6027\u304c\u3042\u308b\u3068\u8a00\u3046\u3002<\/p>\n\n\n\n
\u3053\u306e\u591a\u91cd\u5171\u7dda\u6027\u3092\u907f\u3051\u308b\u305f\u3081\u306bVIF\u306e\u30c1\u30a7\u30c3\u30af\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
VIF\u304c5\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u3001\u591a\u91cd\u5171\u7dda\u6027\u3092\u7591\u3046\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n
10\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u3001\u591a\u91cd\u5171\u7dda\u6027\u304c\u78ba\u5b9a\u7684\u3068\u8003\u3048\u305f\u307b\u3046\u304c\u826f\u3044\u3002<\/p>\n\n\n\n
\u305d\u306e\u5834\u5408\u306f\u3001\u30e2\u30c7\u30eb\u3078\u306e\u540c\u6642\u6295\u5165\u3092\u8ae6\u3081\u305f\u307b\u3046\u304c\u826f\u3044\u3002<\/p>\n\n\n\n
\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n
Multicollinearity and misleading statistical results<\/a><\/p>\n\n\n\n
\u591a\u91cd\u5171\u7dda\u6027 – Wikipedia<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
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\u53c2\u8003\u30b5\u30a4\u30c8<\/h2>\n\n\n\n
\u591a\u91cd\u5171\u7dda\u6027 – Wikipedia<\/a><\/p>\n\n\n\n